[eigen] Custom scalar types and matrix products

[Brad Bell <bradbell@xxxxxxxxxx>]

I am having trouble using the templated scalar type CppAD::AD<Base> with 
eigen's matrix multiply.

To be specific, the code eigen_mul.cpp (included below)
is generating the error message eigen_mul.stderr (included below).
I have reformatted the error message output so that it is easier to read.

A script that:
generates the file build/eigen_mul.cpp,
runs the g++ compiler,
and generates the error message,
can be found at
https://projects.coin-or.org/CppAD/browser/trunk/bug/eigen_mul.sh

You can run this script using the following steps:
    1. svn checkout https://projects.coin-or.org/svn/CppAD/trunk 
cppad_trunk
    2. cd cppad_trunk
    3. mkdir build
    4. cd build
    5. cmake ..
    6. cd ../bug
Then modify the script eigen_mul.sh line
     -I$HOME/prefix/eigen/include
to be the location of the eigen include directory on your machine.
Then execute the command
    ./eigen_mul.sh


eigen_mul.cpp:
=============
#include <Eigen/Core>
#include <cppad/cppad.hpp>

int main() {
     using Eigen::Matrix;
     using Eigen::Dynamic;
     typedef CppAD::AD<double> AScalar;

     Matrix<AScalar, Dynamic, Dynamic> A2(1,1);
     Matrix<AScalar, Dynamic, Dynamic> B2(1,1);

     A2(0,0) = 1.0;
     B2(0,0) = 2.0;

     A2 * B2 * A2;

     return 0;
}

eigen_mul.stderr
================

eigen_mul.cpp:15:12:
warning: ISO C++ says that these are ambiguous,
even though the worst conversion for the first is better than the
worst conversion for the second: [enabled by default]
  A2 * B2 * A2;
            ^
--------------------------------------------------------------------------
/home/bradbell/prefix/eigen/include/Eigen/src/Core/GeneralProduct.h:571:1:
note: candidate 1: const typename

Eigen::ProductReturnType<Derived, OtherDerived>::Type
Eigen::MatrixBase<Derived>::operator*(
     const Eigen::MatrixBase<OtherDerived>&) const

OtherDerived = Eigen::Matrix<CppAD::AD<double>, -1, -1>;
Derived      = Eigen::GeneralProduct<
     Eigen::Matrix<CppAD::AD<double>, -1, -1>,
     Eigen::Matrix<CppAD::AD<double>, -1, -1>, 5>;

typename Eigen::ProductReturnType<Derived, OtherDerived>::Type =
Eigen::GeneralProduct<
     Eigen::GeneralProduct<
          Eigen::Matrix<CppAD::AD<double>, -1, -1>,
          Eigen::Matrix<CppAD::AD<double>, -1, -1>, 5>,
     Eigen::Matrix<CppAD::AD<double>, -1, -1>, 5>

MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const


--------------------------------------------------------------------------
/home/bradbell/prefix/eigen/include/Eigen/src/Core/ProductBase.h:198:1:
note: candidate 2: const

Eigen::ScaledProduct<Derived>
Eigen::operator*(
     const Eigen::ProductBase<Derived, _Lhs, _Rhs>&,
     const typename Derived::Scalar&)

Derived = Eigen::GeneralProduct<
     Eigen::Matrix<CppAD::AD<double>, -1, -1>,
     Eigen::Matrix<CppAD::AD<double>, -1, -1>, 5>;
Lhs = Eigen::Matrix<CppAD::AD<double>, -1, -1>;
Rhs = Eigen::Matrix<CppAD::AD<double>, -1, -1>;

typename Derived::Scalar = CppAD::AD<double>

operator*(
     const ProductBase<Derived,Lhs,Rhs>& prod,
     const typename Derived::Scalar& x
)